This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380450 #52 Jun 28 2025 09:19:39
%S A380450 0,1,1,1,1,2,1,2,1,1,1,2,1,3,2,2,2,2,2,1,3,1,1,2,1,1,3,1,3,2,1,1,2,2,
%T A380450 0,1,2,1,1,1,2,2,0,2,2,2,1,2,2,4,2,2,3,1,3,3,3,3,2,2,3,2,2,2,4,2,0,3,
%U A380450 2,2,1,2,2,2,2,2,3,1,1,2,1,2,1,2,3,1,3,0,2,3
%N A380450 Number of integers k such that prime(n) - primorial(k) is prime.
%C A380450 Conjecture A: Each value occurs an infinite number of times in the sequence.
%C A380450 Conjecture B: All natural numbers occur in the sequence.
%H A380450 Michel Marcus, <a href="/A380450/b380450.txt">Table of n, a(n) for n = 1..5000</a>
%e A380450 For prime(n=6): 13 - 2 = 11, and 13 - 6 = 7, so a(6) = 2.
%t A380450 a[n_]:=Module[{c=0},Do[d=Prime[n]-Fold[Times, 1, Prime[Range[k-1]]];If[PrimeQ[d]&&d>0,c++],{k,n}];c];Array[a,90] (* _James C. McMahon_, Jun 27 2025 *)
%o A380450 (PARI) pri(n) = vecprod(primes(n)); \\ A002110
%o A380450 a(n) = my(nb=0, p=prime(n)); for (k=0, n, if (isprime(p-pri(k)), nb++); ); nb; \\ _Michel Marcus_, Jun 22 2025
%Y A380450 Cf. A385210, A000040, A002110, A175974 (zeros (primes)), A115785 (record positions (primes)).
%K A380450 nonn
%O A380450 1,6
%A A380450 _Daniel D Gibson_, Jun 22 2025
%E A380450 More terms from _Michel Marcus_, Jun 22 2025